This paper presents an approach for obtaining an optimized geometry for the flank of a
tooth by minimizing the equivalent contact stress. The stress calculation method is based
on Hertz theory. As the majority of tooth profiles are involute, the geometric variation
of the flank of the tooth is achieved variationally relative to the involute profile. The
optimum profile is obtained by Monte Carlo simulation. During this optimization, a
polynomial expression of the tooth geometry is used. The parameters influencing the
simulation are the four characteristic contact points. The approach presented has been
applied in a representative case. A study of the geometric sensitivity was conducted on
the optimized tooth profile. Two different approaches were considered: by Monte Carlo
simulation and analytical propagation. The robust and linear nature of the behavior of the
tooth profile was demonstrated when it was subjected to geometric variations.

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